Historically our understanding of the microscopic world has been impeded by limitations
in systems that behave classically. Even today, understanding simple problems
in quantum mechanics remains a dicult task both computationally and experimentally.
As a means of overcoming these classical limitations, the idea of using a
controllable quantum system to simulate a less controllable quantum system has been
proposed. This concept is known as quantum simulation and is the origin of the ideas
behind quantum computing.
In this thesis, experiments have been conducted that address the feasibility of using
devices with a circuit quantum electrodynamics (cQED) architecture as a quantum
simulator. In a cQED device, a superconducting qubit is capacitively coupled to a
superconducting resonator resulting in coherent quantum behavior of the qubit when
it interacts with photons inside the resonator. It has been shown theoretically that
by forming a lattice of cQED elements, dierent quantum phases of photons will
exist for dierent system parameters. In order to realize such a quantum simulator,
the necessary experimental foundation must rst be developed. Here experimental
eorts were focused on addressing two primary issues: 1) designing and fabricating low
disorder lattices that are readily available to incorporate superconducting qubits, and
2) developing new measurement tools and techniques that can be used to characterize
large lattices, and probe the predicted quantum phases within the lattice.
Three experiments addressing these issues were performed. In the rst experiment
a Kagome lattice of transmission line resonators was designed and fabricated, and a
comprehensive study on the eects of random disorder in the lattice demonstrated
that disorder was dependent on the resonator geometry. Subsequently a cryogenic
3-axis scanning stage was developed and the operation of the scanning stage was
demonstrated in the nal two experiments. The rst scanning experiment was conducted
on a 49 site Kagome lattice, where a sapphire defect was used to locally perturb
each lattice site. This perturbative scanning probe microscopy provided a means to
measure the distribution of photon modes throughout the entire lattice. The second
scanning experiment was performed on a single transmission line resonator where a
transmon qubit was fabricated on a separate substrate, mounted to the tip of the
scanning stage and coupled to the resonator. Here the coupling strength of the qubit
to the resonator was mapped out demonstrating strong coupling over a wide scanning
range, thus indicating the potential for a scanning qubit to be used as a local quantum
probe.